plumiRoots of quadratic equations: Edexcel International A Level Further Maths questions
Every Edexcel International A Level Further Maths exam question on FP1.2 Roots of quadratic equations, 2019–2025, with its mark scheme and examiner’s report.
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All 11 questions on Roots of quadratic equations, as a list
- June 2025, Further Pure 1 (FP1), Q6 (11 marks): f (x) = 3x 2 + kx – 5 where k is a constant. The equation f (x) = 0 has roots α and β. (a) State the value of αβ. Given that α + β = 9αβ (b) determine the value
- January 2025, Further Pure 1 (FP1), Q3 (7 marks): The quadratic equation 3 2 5 0 2 x x has roots α and β Without solving the equation, (a) write down the value of (α + β) and the value of αβ (b) determine the v
- June 2024, Further Pure 1 (FP1), Q5 (9 marks): The equation 5x 2 – 4x + 2 = 0 has roots 1 p and 1 q (a) Without solving the equation, (i) show that pq = 5 2 (ii) determine the value of p + q (b) Hence, witho
- January 2024, Further Pure 1 (FP1), Q5 (9 marks): The quadratic equation 2x 2 – 3x + 7 = 0 has roots α and β Without solving the equation, (a) write down the value of (α + β) and the value of αβ (b) determine t
- June 2023, Further Pure 1 (FP1), Q5 (10 marks): f(x) = x 2 – 6x + 3 The equation f(x) = 0 has roots α and β Without solving the equation, (a) determine the value of (α 2 + 1) (β 2 + 1) (b) find a quadratic eq
- January 2023, Further Pure 1 (FP1), Q5 (9 marks): The quadratic equation 4 3 0 2 x x k where k is an integer, has roots α and β (a) Write down, in terms of k where appropriate, the value of α + β and the value
- June 2022, Further Pure 1 (FP1), Q5 (10 marks): The quadratic equation 2x2 – 3x + 5 = 0 has roots α and β Without solving the equation, (a) write down the value of (α + β) and the value of αβ (b) determine th
- January 2022, Further Pure 1 (FP1), Q6 (8 marks): The quadratic equation Ax 2 + 5x – 12 = 0 where A is a constant, has roots α and β (a) Write down an expression in terms of A for (i) α + β (ii) αβ The equation
- October 2021, Further Pure 1 (FP1), Q3 (9 marks): The quadratic equation 2x 2 – 5x + 7 = 0 has roots α and β Without solving the equation, (a) write down the value of (α + β) and the value of αβ (b) determine,
- January 2021, Further Pure 1 (FP1), Q4 (8 marks): The equation 2x2 + 5x + 7 = 0 has roots α and β Without solving the equation (a) determine the exact value of α3 + β3 (b) form a quadratic equation, with intege
- October 2020, Further Pure 1 (FP1), Q2 (9 marks): The quadratic equation 5x2 – 2x + 3 = 0 has roots α and β. Without solving the equation, (a) write down the value of (α + β) and the value of αβ (b) determine,
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